Memoirs presented to the Cambridge philosophical society on the occasion of the jubilee of Sir George Gabriel Stokes, bart., Hon. LL. D., Hon. SC. D., Lucasian professor.

OF THE FIRST KIND OF TOTAL DIFFERENTIALS. 347
ordinary double points), but in this case the singularity of the section is of a higher order,
one of the branches having an inflexion, so that the singularity is equivalent to three
ordinary double points. In the quartic case the section is a cubic and a tangent to it at
an inflexion.
When the surface is birationally transformed into the cone (E') the generators of
the cone correspond to a family of twisted cubics on the quartic. For to the generator
'=Xy', y' = uz' (where X, /. are connected by a cubic equation), corresponds in the
x, y, z, w space the variable part of the curve of intersection of the quadrics z2= Xxw,
w2 = ~yz; but these have in common the fixed straight line z - w = O, so that their
residual curve of intersection is a twisted cubic.
44-2